Haldane is today best remembered for a body of mathematical work with singular importance for twentieth-century biology. Together with the English statistician Ronald Fisher and the American geneticist Sewall Wright, Haldane formed a triumvirate that turned evolutionary biology from a domain of naturalists like Darwin into an exact, mathematical science.
Darwin’s key insight—that all life emerged from a common ancestor with a lot of help from natural selection—is well known.5 Less well known is the sheer breadth of supportive evidence that his naturalist’s mind amassed. This evidence includes the spectacular success of breeders, whose artificial selection brought forth attractive roses and productive wheat, as well as dogs as different as pugs and Rottweilers.6 The evidence also includes an endless procession of ever-changing fossil forms, from traces of primitive worms in the most ancient of rocks to sophisticated invertebrates like ammonites and more recent life-forms like fishes, amphibians, reptiles, and eventually mammals. It includes the anatomy of animals as superficially different as rats and bats, whose skeletons are variants of the same blueprint and reveal their deep relatedness. It includes useless atavistic traits like the rudimentary eyes of fish whose ancestors took up residence in dark caves and the embryonic teeth of birds, which first grow and later melt away again—remnants of birds’ toothy reptilian ancestors.
And Darwin’s evidence includes the motley collections of species found on remote islands like Hawaii or the Galapagos—profuse in unusual birds, insects, and bats but impoverished in mammals and amphibians. This contrast is mystifying until one realizes that island faunas are not the febrile dream of a mad creator. Instead, they contain those continental species that can get there by wind or flight and are liberated from competition to radiate into a cornucopia of new forms.7
Darwin’s theory emboldened naturalists to search for further evidence of evolution in action, and they did not have to search long before they found the intriguing case of the peppered moth Biston betularia. Like so many other organisms favored by biologists—for example, the tiny fruit fly Drosophila and the even tinier bacterium Escherichia coli—the peppered moth is anything but flashy. It is a perfectly inconspicuous inhabitant of our planet, and that’s the point: it aims to fit in. The grainy salt-and-pepper speckles on its gray wings are perfect camouflage on the lichen-covered tree bark in its English habitat. The moth is possibly the most literal illustration of the term “survival of the fittest” that one could find.8 Moths with speckled wings fit a tree’s texture best—they are best adapted to the tree’s surface—and thus stand a better chance of eluding the sharp eyes of predatory birds. Experiments that pin moths to a tree and monitor how often they get eaten by birds prove just that: in a forest of light-barked trees, darker moths get eaten more often. They are less fit, less well adapted.9
Dark moths arise from occasional DNA mutations that alter a gene affecting wing color. Such mutations create a new form—a new allele—of this gene, which helps turn the wing darker and exposes the moths to predators. The misfortune of dark moths changed after the start of the Industrial Revolution, when trees became increasingly covered in black soot that concealed dark moths and revealed light moths to predatory birds. Dark moths carrying this new allele were better adapted to polluted trees, and more of them survived bird attacks. As air pollution increased and covered more trees in soot, dark moths spread at the expense of their lighter brethren until they became the prevalent forms in polluted areas.
Together, short-lived moths, their large populations, and a quickly changing environment offered an opportunity for mathematically inclined scientists like Haldane. In the industrial town of Manchester, dark-winged moths had completely replaced light-winged moths within half a century. Knowing this, Haldane developed mathematical equations that allowed him to calculate how much more likely it was that a light moth would be eaten by a bird than a dark moth. The answer turned out to be about 30 percent.10 This modest difference in fitness sufficed to transform an entire population’s wing color within a human life span.11
The wing colors of the peppered moth are discrete variants, each caused by a different allele with a major effect on color. But most variation in nature is not like that. It is graded, continuous variation, like the many hues of green in the trees of a forest, the innumerable shades of brown in the coats of dogs, the wide-ranging sizes among different grains of wheat, and the extensive differences in human stature, from the famously short Pygmies to the famously tall Dutch people. This is polygenic variation, influenced by not just one but hundreds of genes, each with a tiny effect.
Here is where the second member of our triumvirate, Ronald Fisher, comes in. A Cambridge-trained mathematician, he helped father not only modern statistics, but also population genetics (and eight children, to boot). Fisher worked for ten years at Rothamstead, an agricultural research station. There, he analyzed data from plant breeders, which helped him extend Haldane’s mathematical feat from discrete variation to such polygenic traits as height or yield. He demonstrated mathematically how strong selection must be—how many individuals must be culled from a herd of cows, what fraction of wheat plants should be allowed to survive—to predict how fast traits like milk yield and grain size could evolve in one generation. Not only was Fisher’s work useful, its mathematical precision also made it a capstone to much of Darwin’s work.
Sewall Wright, the third member of the triumvirate, worked in parallel to Fisher and Haldane. Like Fisher, Wright was tackling practical problems in agriculture, in his case about breeding the most productive cows, hogs, and sheep. But unlike the theoretician Fisher, Wright was not just mathematically adept, but also a dyed-in-the-wool experimentalist who performed breeding experiments on more than thirty thousand guinea pigs. (The milk yield of guinea pigs may interest no one, but they are vastly superior to cows for breeding experiments because they are smaller, reproduce faster, and can be kept in larger populations.) And during these experiments Wright noticed something odd: selecting the best animals for reproduction—Fisher’s prescription for breeding success—when repeated over and over for multiple generations, did not always work well to create a superior breed. For example, during ongoing selection to improve one trait, like beef quality or milk yield, other traits often deteriorate, including two crucial ones: mortality and fertility. And when that happens, a breeder’s greatest hope may have become just another evolutionary dead-end.
Wright also investigated more than a hundred years of pedigrees and records kept by animal breeders. All this data helped him see what the theoretician Fisher had missed: genes interact in mind-bogglingly complex ways. A gene that increases milk yield can reduce meat quality, another one that increases meat quality may reduce fertility, and a third one that increases fertility may also increase a cow’s risk of dying from disease. And Wright’s mathematical analysis taught him that these interactions are the reason why natural selection, although essential, need not be sufficient for evolution’s progress.12
You might ask what guinea pigs and dairy cows could possibly teach us about how nature creates. The creative powers of animal breeding do indeed seem modest when we view breeds of cattle and varieties of corn against the millions of species in life’s glorious diversity. But Darwin himself already reminded us in the Origin of Species of how much diversity human breeders have created in some species. A modern corn cob is barely recognizable as a descendant of its grass-like ancestor teosinte from Middle America, and Chihuahuas are so different from Great Danes that it stretches the imagination to call them members of the same species. The success of breeding is a microcosm of evolution’s creative power, and it uses the same principles that evolution has employed for almost four billion years. This is why Wright’s insights eventually helped us understand nature’s creativity on a larger scale.
In 1932, Wright was invited to present his work at the Sixth International Congress of Genetics to a general audience of biologists. Unfortunately, the mathematics were beyond the average biologist’s
skill, and Wright needed to communicate his ideas in a more accessible way.13
This is how the fitness landscape was born.
A fitness landscape, also known as an adaptive landscape, is a visualization that allows us to picture evolution at work. It looks much like a topographic map of a mountain range, except that its axes—corresponding to the east–west and north–south dimensions of a map—describe different characteristics of an organism that can vary over a continuous range of values. Such characteristics might include a giraffe’s height, a rose petal’s color, or the wing coloration of the peppered moth, as shown on the horizontal axis in Figure 1.1. An organism at one location in the landscape has a specific trait value, such as a wing with a specific shade of gray. A DNA mutation that creates a different shade of gray moves the organism along one axis of the landscape. The vertical dimension in the landscape corresponds not to altitude but to the fitness that comes with the trait value. In the years before industrial soot soiled English forests, lighter moths fit the tree background better than darker moths, so they occupied higher elevations closer to the landscape’s peak.
Figure 1.1.
Even a highly simplified two-dimensional landscape like that of Figure 1.1 already confers useful information. For example, the landscape has a single hump or “peak” close to the light end of the gray scale. All-black moths are easily picked off by birds, hence their fitness—on the far left—is far below peak. At the other extreme, snow-white moths also have some handicap because they are not perfectly matched to the mottled pattern of lichen-covered trees.
Over multiple generations, an evolving population of moths can be driven across this landscape by various evolutionary forces. One such driving force is DNA mutation, which creates new alleles. Mutation is blind, so a moth becomes either lighter or darker regardless of whether being lighter or darker would be the better move. A second force is natural selection—those moths who occupy the lowest parts of the slope farthest from the peak are most likely to get eaten by birds. Jointly, mutation and selection herd a population toward a peak, where most individuals are well adapted and resemble each other. Selection then keeps the population near the peak by culling those mutant outliers that are too far downslope.
As the environment changes, the locations of the peaks in a landscape can change, too. For example, the climate may become hostile to moths, or a new predator can appear, or pollution can transform lichen-covered trees into soot-covered trees. In this latter case, the landscape’s peak shifts such that dark moths are preferred over light moths, as shown in Figure 1.2. The combined action of mutation and selection are still at work, but now they drive the population in the opposite direction, up the new peak.
Figure 1.2.
This simple visualization of what natural selection does—it drives a population up a landscape’s peak—helped spread Wright’s ideas among biologists. Wright used the landscape as a metaphor and was deliberately vague about the traits it could represent.14 That turned out to be fortuitous because it allowed the landscape concept to become a veritable Rorschach inkblot for evolutionary biologists, permitting ever-evolving interpretations of the basic idea. Among the first who realized its broad explanatory power was the paleontologist George Gaylord Simpson, who used landscapes to describe evolutionary transformations that were more ancient and glacially slower than the recent and swift evolution of the peppered moth. In his 1944 book, Tempo and Mode in Evolution, Simpson illustrated the idea of a fitness landscape with today’s horses and their fifty-five-million-year-long evolution from a diminutive ancestor.15 This ancestor was the dog-sized Eohippus—literally “dawn horse.” Eohippus had teeth typical of animals that feed on soft leaves, protected by only a thin layer of the rock-hard enamel that prevents abrasion. During the Miocene, some twenty million years ago, grasslands expanded and forests receded, which created new habitats for horses. Feeding on grass rather than foliage, however, requires teeth that can resist the wear and tear caused by the harder grass blades. Horses ascended the new fitness peak by evolving increasingly thick enamel, piled higher and higher on their teeth, which led to the high-crowned teeth of today’s horses.16
Wright had also shown that not all adaptive landscapes are single-peaked like that of Figure 1.1, and that landscapes with two or more peaks can arise from complex interactions among genes. A two-peaked landscape was conquered by another group of ancient organisms: the now extinct spiral-shaped mollusks known as ammonites.17 As an ammonite grew, it expanded its shell by adding material to the shell’s growing rim, and it eventually secreted a wall—visible as a rib-like suture on the outer surface—to seal the shell’s outermost part from its interior. Through multiple episodes of growth and wall building, the animal created a series of ever-larger sealed compartments that spiraled around a central axis (Figure 1.3). Unlike snail shells, ammonite shells were multi-chambered, but the animal inhabited only the outermost chamber. This chamber connected to the others through a siphuncle, a thin tube used to empty or fill these chambers, much like a submarine’s ballast tanks, allowing the animal to rise toward the surface or descend into the depths of the ocean.
Although the soft parts of ammonites are rarely preserved, we can get an idea of how these animals propelled themselves through the water from a present-day relative, the nautilus. Ancestors of the nautilus discovered the principle of jet propulsion, which the nautilus still exploits, expelling water through a tube-like syphon near its mouth to push itself backward through the water.18 Pushing your home through the water uses a lot of energy, and because energy is scarce out in the wild blue, it is important that a nautilus or an ammonite swims as efficiently as possible. A home with the right shape is crucial to achieving this efficiency.
Figure 1.3.
Even though ammonites come in many sizes and shapes, the paleontologist David Raup realized in 1967 that these shapes could be categorized by two simple quantities. The first is the rate at which an ammonite increases its diameter while it grows and adds chambers, and the second is related to the diameter of the largest chamber opening, which is its gateway to the outside world.19 A prototypical ammonite has the shape shown in the photograph on the left side of Figure 1.3, but other shapes also occur.20 For example, ammonites that expand their diameter very slowly but have large chamber openings would resemble the one in the middle of Figure 1.3, whereas the opposite extreme—fast expansion and small opening—would correspond to the shape on the right side of the figure.
These two quantities are the two axes of a three-dimensional fitness landscape. The elevation reflects how easily an ammonite can propel itself through the ocean. John Chamberlain, a graduate student of Raup, was the first who measured this swimming efficiency.21 He created dozens of Plexiglas models of various ammonite shapes and dragged them through a water tank to measure their drag coefficient, which is directly proportional to the amount of force needed to propel an animal through the water. The higher the drag coefficient, the more energy the animal needs in order to swim at a given speed.22
Chamberlain found that ammonites were ten times less efficient swimmers than those truly streamlined animals with an internal skeleton, like squid, fish, and dolphins.23 That’s the price they paid for being protected by a hard external skeleton. But swimming efficiency also varied among ammonites. This means that the three-dimensional fitness landscape of swimming efficiency is not flat. In fact, it turns out that the landscape has two peaks, a bit like the landscape shown in Figure 1.4.24 That is, two distinct ammonite shapes are more efficient than all other shapes. The peaks corresponding to these shapes are separated by a valley of inferior shapes. If evolution has optimized ammonite shape for efficient swimming, then actual ammonite shapes should cluster near the peaks. Otherwise, they should be scattered haphazardly across the peaks and valleys.
To find out which was the case, Raup and others analyzed shape data from hundreds of ammonites, but they were in for a surprise. They found a third, unexpected possibility: the ammonites clustered a
round only one peak. The other one was mysteriously vacant. This could have happened if no mutations had ever created ammonite shapes near the vacant peak. In that case, natural selection would have had nothing to select, so the peak would have remained unoccupied. But the actual solution to this mystery was more mundane: a lack of data. By 2004, when scientists had recorded the shapes of hundreds of additional ammonites, they found the second peak well occupied after all.25 Among all possible ammonite shapes, evolution favored the two that swam most efficiently. In Wright’s genetic language, the two peaks would correspond to different combinations of genes that helped create two different but equally optimal shapes for swimming. Sadly, we may never know which genes, nor how ammonites climbed those peaks, because they all died so many millions of years ago.
Figure 1.4.
The fitness landscapes of ammonites, horse teeth, and peppered moths are built on the hard foundation of physics—the hydrodynamics of swimming, the mechanics of mastication, and the optics of camouflage. But other fitness landscapes are grounded in the softer realities of animal behavior, for example in a genus of flashy tropical butterflies known as Heliconius, the passion-vine butterflies.
One could be forgiven for wondering why a slow-flying, delicate creature like a butterfly would not adopt the same strategy that has guaranteed the survival of the peppered moth through the millennia: hide. That’s because passion-vine butterflies do exactly the opposite. Coming in a profusion of resplendent wing colorations, they aim to show off. Some species sport a single red stripe on a solid black wing, a minimalist pattern of sleek elegance, some add a splash of yellow, others a fan of red rays radiating from the body, and yet others parade a sunburst of bright orange and yellow patches.
Life Finds a Way Page 2
